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A154244
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a(n) = 6*a(n-1) - 2*a(n-2) for n>1; a(1)=1, a(2)=6.
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11
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1, 6, 34, 192, 1084, 6120, 34552, 195072, 1101328, 6217824, 35104288, 198190080, 1118931904, 6317211264, 35665403776, 201358000128, 1136817193216, 6418187159040, 36235488567808, 204576557088768, 1154988365396992
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OFFSET
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1,2
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COMMENTS
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lim_{n -> infinity} a(n)/a(n-1) = 3+sqrt(7) = 5.6457513110....
a(n) equals the number of words of length n-1 over {0,1,2,3,4,5} avoiding 01 and 02. - Milan Janjic, Dec 17 2015
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LINKS
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FORMULA
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a(n) = ((3 + sqrt(7))^n - (3 - sqrt(7))^n)/(2*sqrt(7)).
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MATHEMATICA
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a[n_]:=(MatrixPower[{{1, 3}, {1, 5}}, n].{{1}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *)
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PROG
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(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-7); S:=[ ((3+r)^n-(3-r)^n)/(2*r): n in [1..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 07 2009
(Magma) I:=[1, 6]; [n le 2 select I[n] else 6*Self(n-1)-2*Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 02 2012
(Sage) [lucas_number1(n, 6, 2) for n in range(1, 22)] # Zerinvary Lajos, Apr 22 2009
(Maxima) a[1]:1$ a[2]:6$ a[n]:=6*a[n-1]-2*a[n-2]$ makelist(a[n], n, 1, 21); // Bruno Berselli, May 30 2011
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CROSSREFS
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Equals 1 followed by 2*A010913 (Pisot sequence E(3,17)).
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KEYWORD
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nonn,easy
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AUTHOR
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Al Hakanson (hawkuu(AT)gmail.com), Jan 05 2009
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EXTENSIONS
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STATUS
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approved
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